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Linear rank preservers on infinite triangular matrices

Roksana Slowik
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회지 (Journal of the KMS)|제53권 제1호|pp. 73-88

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키워드

infinite triangular matriceslinear rank preservers
주제분류수학

초록

We consider $\mc T_\infty(F)$ -- the space of all infinite upper triangular matrices over a field $F$. We give a description of all linear maps that satisfy the property: if $\rank(x)=1$, then $\rank(\phi(x))=1$ for all $x\in\mc T_\infty(F)$. Moreover, we characterize all injective linear maps on $\mc T_\infty(F)$ such that if $\rank(x)=k$, then $\rank(\phi(x))=k$.

Abstract

We consider $\mc T_\infty(F)$ -- the space of all infinite upper triangular matrices over a field $F$. We give a description of all linear maps that satisfy the property: if $\rank(x)=1$, then $\rank(\phi(x))=1$ for all $x\in\mc T_\infty(F)$. Moreover, we characterize all injective linear maps on $\mc T_\infty(F)$ such that if $\rank(x)=k$, then $\rank(\phi(x))=k$.

참고문헌 (18)

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관련 논문AI추천

INJECTIVE LINEAR MAPS ON T1(F) THAT PRESERVE THE ADDITIVITY OF RANKRoksana Slowik대한수학회 · 대한수학회보2017 · 제54권 제1호EXTREME PRESERVERS OF MAXIMAL COLUMN RANK INEQUALITIES OF MATRIX MULTIPLICATIONS OVER SEMIRINGS박권룡, 송석준, L. Hernandez Encinas대한수학회 · 대한수학회지2010 · 제47권 제1호Linear preservers of spanning column rank of matrix products over semirings송석준, 전영배, 천기상대한수학회 · 대한수학회지2008 · 제45권 제4호Linear preservers of spanning column rank of matrix sums over semirings송석준대한수학회 · 대한수학회지2008 · 제45권 제2호LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES강경태, 송석준, Leroy B. Beasley대한수학회 · 대한수학회지2015 · 제52권 제3호COMPOUND-COMMUTING ADDITIVE MAPS ON MATRIX SPACESWai Leong Chooi대한수학회 · 대한수학회지2011 · 제48권 제1호

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